Question

The table below represents the data collected at a sandwich shop for the last six months with respect to the type of bread people ordered (sourdough or wheat) and whether or not they got cheese on their sandwich.

What is the P(cheese | wheat) ? Show all work to receive full credit.

Answer 1

The number of times people got cheese and wheat is 1200

Explanation:

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Answer 2

`\sf (12)/(19)`

Explanation:

To begin, add the column and row totals to the table (see attachment).

Let W = Wheat

Let C = With cheese

`\sf Probability\:of\:an\:event\:occurring = (Number\:of\:ways\:it\:can\:occur)/(Total\:number\:of\:possible\:outcomes)`

`\implies \sf P(W)=(1900)/(3125)=(76)/(125)`

`\implies \sf P(C)=(2000)/(3125)=(16)/(25)`

`\implies \sf P(W \cap C)=(1200)/(3125)=(48)/(125)`

As the events W and C are not independent, we can use the formula:

`\sf P(C\: | \:W)=(P(W \cap C))/(P(W))`

Substituting the values into the formula:

`\sf P(C\: | \:W)=((48)/(125))/((76)/(125))=(48)/(76)=(12)/(19)`